What is the ruling concerning blood that appeared ten days after menstruation, continued for five days as blood, and three days as a brownish discharge, and does my wife have to make up the prayers she missed during that period?

If a woman's menstrual period is seven days, then she becomes pure for ten days, and then bleeding resumes for five days, the resuming blood is not menses. This is because the total number of days (7 + 10 + 5) exceeds fifteen days (the maximum duration of menses), and because the intervening period of purity (10 days) is less than fifteen days (the minimum duration of purity). Therefore, it is irregular bleeding (istihadah) which does not prevent prayer. She must make up the prayers for the days she considered to be menses. The opinion of the majority concerning the importance of making them up is more cautious.